1 the lipton tea company pack tea in bags marked as 100g A l

1.) the lipton tea company pack tea in bags marked as 100g. A large number of packs of tea were weighted and the mean and standard deviation were calculated as 105 g and and 2.5g respectively. assuming this data is normally distributed, what percentage of packs are underweight?

2.)68% of students and a school weight between 52 kg and 80kg. Assuming this data is normally distributed what are the mean and standard deviation?

Solution

Normal Distribution
I)
Mean ( u ) =105
Standard Deviation ( sd )=2.5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 100) = (100-105)/2.5
= -5/2.5= -2
= P ( Z <-2) From Standard Normal Table
= 0.0228 ~ 2.28% are underweight

II)
                  
Given that the mean (u) of a normal probability distribution is X and the
standard deviation (sd) is Y.
(a) About 68% of the area under the normal curve is within one standard deviation of the mean. i.e.
(u ± 1s.d)
So to the given normal distribution about 68% of the observations lie in between
= (X ± Y)
X - Y = 52 ; X +Y = 80
SOLVING (1)+(2) => 2X = 132 => X = 66; Y = 66 - 52 = 16; Mean = 66, s.d = 16